Final answer:
Changing the exhaust nozzle area of a turbine engine can impact its efficiency and thrust, and when turbines at a power plant are upgraded, the change in efficiency leads to more electrical energy output and less heat transfer to the environment. Efficiency improvements are also linked to entropy changes within the system.
Step-by-step explanation:
Changing the exhaust nozzle area of a turbine engine affects the exhaust flow characteristics, which in turn impacts the engine efficiency and thrust. A larger nozzle area might reduce exhaust velocity, leading to less thrust, while a smaller nozzle can increase the exhaust velocity, resulting in more thrust. Considering the principles of momentum and energy conservation, the nozzle design must match the engine's operating conditions to optimize performance. Moreover, when dealing with power plants, turbine efficiency plays a crucial role in determining how much electrical energy is produced and how much heat is transferred to the environment.
When turbines at a coal-powered power plant are upgraded, leading to a 3.32% increase in efficiency, we can calculate the additional electrical energy produced and the reduced heat transfer to the environment. If the previous efficiency was 36% and the heat transfer into the engine remains constant at 2.50×10¹⁴ J, the upgraded efficiency becomes 39.32%. The difference in electrical energy output and heat transfer due to increased efficiency can be computed using thermodynamic equations and considering that efficiency is related to the temperatures of the hot and cold reservoirs of the engine.
It is important to note that the efficiency of heat engines is invariably tied to the concept of entropy, which is a measure of the unavailability of a system's energy to do work. A higher entropy signifies more waste heat and less usable work, hence reduced efficiency.